off a cliff and it takes 10 seconds to hit the ground, your last thought will be, "hey, it took-- i bet you i fell 500 meters." that's how far you'd go. and you see that. any questions on all this? so we're really summarizing what we talked about last time. there's a difference between how much you pick up speed, okay, and between how fast you're going and how far you're going. and for falling things, the acceleration will always be the same, 10 meters per second per second. later on we'll round that off to 9.8 meters per second, per second, okay? but 10s are easier to deal with, right? and we find out that how fast we go is simply the acceleration multiplied to how long you're falling. it makes sense. and how far you go has to do with the time squared. so it's averaging out 5t squared. how we got that is derived in the footnote of your book, and you can kind of go back and look at that if you want. i don't expect you to derive that. i want you to just know this doesn't pop out of the air and magic, okay? there's a reason for this. now, we talked how that came about last time. look it u